Fuzzy controller designs are based on using a knowledge-base (KB) which consists of fuzzy rules and membership functions. To utilize this KB, existing designs of fuzzy controllers employ approximate reasoning mechanisms such as the Compositional Rule of Inference (CRI) which requires the formation of fuzzy matrices. The fuzzy matrices grow in complexity as the number of inputs/outputs of the controller increases, thereby requiring larger memory and more intensive computations. For all input signals of the fuzzy controller to contribute to its output, the scheme evaluates all the rules to make its decision giving rise to high computational requirements and coarser approximation. At the defuzzifier each rule is associated with one membership function (MF) value, which is identified herein as membership grade (MG). The scheme utilizes these MG's to calculate the controller output. To obtain the final output of the controller, all the possible rules are fired giving rise to many outputs, and these outputs are then averaged using special methods.
Due to the above, fuzzy controllers, even though powerful, are difficult to optimize and generally face difficulties in coping with real-time applications for fast and complex multivariable processes.
It can be seen, therefore, that using a scheme which reduces the number of rules that the fuzzy controller requires to fire, as well as employing a defuzzification method whose average is less coarse will result in a fuzzy controller with an improved response, easier to tune and requires much less memory for processing its knowledge-base.
Other relevant literature includes:
1. L. Sultan and T. H. Janabi, "Fuzzy Logic Controller", U.S. Pat. No. 5,499,319; 1996. PA0 2. L. A. Zadeh, "Outline of a new approach to the analysis of complex systems and decision processes," IEEE Trans. Systems, Man and Cybernetics, Vol. SMC-3, pp. 28-44, 1973. PA0 3. L. A. Zadeh, "The concept of a linguistic variable and its application to approximate reasoning, I and II", Inform. Sci., Vol. 8, pp. 199-249 and vol. 9, pp. 301-357, 1975. PA0 4. L. A. Zadeh, "Fuzzy Logic", IEEE Computer Magazine, pp. 83-93, Apr. 1988. PA0 5. L. A. Zadeh, "Knowledge Representation in Fuzzy Logic", IEEE Transaction on Knowledge and Data Engineering, Vol. 1, No. 1, pp. 89-100, March 1989. PA0 6. E. H. Mamdani, "Application of Fuzzy Logic to Approximate Reasoning Using Linguistic Synthesis", IEEE Transaction on Computer, Vol. C-26, No. 12, pp. 1182-1191, December 1977. PA0 1. It is a controller for general purpose applications capable of solving linear and nonlinear control problems. PA0 2. The controller can fire as few, or as many, fuzzy rules as desired, hence it can be configured to have fast real-time response. PA0 3. There is reduced memory requirement. PA0 4. The controller can solve complex and multivariable control applications.